Time Value of Money Annuities

Ordinary Annuity Annuity Due 1 2 3 i% PMT PMT PMT 1 2 3 i% PMT PMT PMT page-2 Ordinary Annuity 1 2 3 i% PMT PMT PMT Annuity Due 1 2 3 i% PMT PMT PMT PV FV 17

What’s the FV of a 3-year ordinary annuity of $100 at 10%? page-3 What’s the FV of a 3-year ordinary annuity of $100 at 10%? 1 2 3 10% 100 100 100 18

Financial Calculator Solution page-4 Financial Calculator Solution INPUTS N I/YR PV PMT FV OUTPUT Have payments but no lump sum PV, so enter 0 for present value. 19

What’s the PV of this ordinary annuity? page-5 What’s the PV of this ordinary annuity? 1 2 3 10% 100 100 100 20

Have payments but no lump sum FV, so enter 0 for future value. page-6 INPUTS N I/YR PV PMT FV OUTPUT Have payments but no lump sum FV, so enter 0 for future value. 21

Find the FV and PV if the annuity were an annuity due. page-7 Find the FV and PV if the annuity were an annuity due. 1 2 3 10% 100 100 100 22

Switch from “End” to “Begin”. page-8 Switch from “End” to “Begin”. Then enter variables to find PVA3 = $273.55. INPUTS N I/YR PV PMT FV OUTPUT 23

Switch from “End” to “Begin”. page-9 Switch from “End” to “Begin”. Then enter variables to find FVA3 = $364.10. INPUTS N I/YR PV PMT FV OUTPUT Switch your calculator from begin mode back to end mode. 23

page-10 Show on the number line where the PV of the annuity due and the FV of the annuity due are calculated. 1 2 3 10% 100 100 100 22

Calculations using Excel (in edit mode, double click on the insert below for Excel) page-11

Calculations using Excel (in edit mode, double click on the insert below for Excel) page-12

Calculations using Excel (in edit mode, double click on the insert below for Excel) page-13

What is the PV of this uneven cash flow stream? page-14 What is the PV of this uneven cash flow stream? 1 2 3 4 10% 100 300 300 -50 90.91 247.93 225.39 -34.15 530.08 = PV 24

Input in “CFLO” register: Press CF page-15 Input in “CFLO” register: Press CF CF0 = 0 ENTER CF1 = 100 ENTER CF2 = 300 ENTER CF3 = 300 ENTER CF4 = -50 ENTER Press NPV button I = 10% ENTER CPT NPV = 530.09. (Here NPV = PV.) 25

Calculations using Excel (in edit mode, double click on the insert below for Excel) page-16